The Beresinskii-Kosterlitz-Thouless transition is expected to describe the metal-to-superconductor thermal transition in quasi-2D systems. However, despite many efforts along the years its signatures remain rather elusive. In this second lectures I will give an overview of the numerous attempts we made along the years to identify the mechanisms which may hinder a clear-cut observation of BKT physics in 2D films of conventional and unconventional superconductors. In particular I will discuss the role of the vortex-core energy and of the spontaneous inhomogeneity of the superconducting background which naturally emerge in disordered thin films. These effects must be seriously taken into account while addressing the famous universal jump of the superfluid density, the non-linear IV characteristics near Tc, or the paraconductivity effects while approaching it from above. Finally, I will make a comparison with some recent results within the context of cold atoms, underlying differences and analogies between the two classes of systems.